论文标题
布朗运动及其概括性的衰老弧形法律
Aging arcsine law in Brownian motion and its generalization
论文作者
论文摘要
经典的弧形定律指出，布朗运动的正或负面占用时间的一部分不会融合到常数，而是在分布中收敛到弧菌分布。在这里，我们考虑系统的制备如何影响Arcsine法律，即Arcsine Law的老化。我们在布朗运动中得出了占用时间统计的老化分布定理，其中测量时间与测量时间开始在确定分布的形状方面起着重要作用。此外，我们表明该结果可以推广为在更新过程中的衰老分布极限定理。
Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as aging distributional limit theorem in renewal processes.
